Reservoir flow simulation typically uses a 3D static model of a reservoir. This static model includes a 3D stratigraphic grid (S-grid) commonly comprising millions of cells wherein each individual cell is populated with properties such as porosity, permeability, and water saturation. Such a model is used first to estimate the volume and the spatial distribution of hydrocarbons in place. The reservoir model is then processed through a flow simulator to predict oil and gas recovery and to assist in well path planning.
In petroleum and groundwater applications, realistic facies modeling, prior to porosity, permeability, and water saturation modeling, is critical to make realistic flow performance predictions that will enable identifying new resource development opportunities and make appropriate reservoir management decisions such as new well drilling. Current practice in facies modeling is mostly based on variogram-based simulation techniques. A variogram is a statistical measure of the correlation between two spatial locations in a reservoir. A variogram model is usually inferred from well data.
These variogram-based simulation techniques are known to give to a modeler a very limited control on the continuity and the geometry of simulated facies. The techniques may provide reasonable predictions of the subsurface architecture in the presence of closely spaced and abundant data, but they usually fail to adequately model reservoirs with sparse data collected at a limited number of wells. This is commonly the case, for example, in deepwater exploration and production where, in general, variogram-based models display much more stochastic heterogeneity than expected from the conceptual depositional models provided by geologists.
A more recent modeling approach, referred to as multiple-point statistics simulation, or MPS, has been proposed by Guardiano and Srivastava, Multivariate Geostatistics: Beyond Bivariate Moments: Geostatistics-Troia, in Soares, A., ed., Geostatistics-Troia: Kluwer, Dordrecht, V. 1, p. 133–144. (1993). MPS simulation is a reservoir facies modeling technique that uses conceptual geological models as 3D training images to generate geologically realistic reservoir models. Reservoir models utilizing MPS methodologies have been quite successful in predicting the likely presence and configurations of facies in reservoir facies models.
Numerous others publications have been published regarding MPS and its application. Caers, J. and Zhang, T., 2002, Multiple-point Geostatistics: A Quantitative Vehicle for Integrating Geologic Analogs into Multiple Reservoir Models, in Grammer, G. M et al., eds., Integration of Outcrop and Modern Analog Data in Reservoir Models: MPG Memoir. Strebelle, S., 2000, Sequential Simulation Drawing Structures from Training Images: Doctoral Dissertation, Stanford University. Strebelle, S., 2002, Conditional Simulation of Complex Geological Structures Using Multiple-Point Statistics: Mathematical Geology, V. 34, No. 1. Strebelle, S., Payrazyan, K., and J. Caers, J., 2002, Modeling of a Deepwater Turbidite Reservoir Conditional to Seismic Data Using Multiple-Point Geostatistics, SPE 77425 presented at the 2002 SPE Annual Technical Conference and Exhibition, San Antonio, September 29–October 2. Strebelle, S. and Journel, A, 2001, Reservoir Modeling Using Multiple-Point Statistics: SPE 71324 presented at the 2001 SPE Annual Technical Conference and Exhibition, New Orleans, September 30–October 3. Training images used in MPS simulation describe geological structures believed to be present in the subsurface. The training images do not carry any spatial information of the actual field; they only reflect a prior geological conceptual model. Traditional object-based algorithms, freed of the constraint of data conditioning, can be used to generate such images. MPS simulation consists then of extracting patterns from the training image, and anchoring them to local data, i.e. well logs. Incorporating geological interpretation into reservoir models, as performed by MPS simulation using training images, is particularly important in areas with few drilled wells.
A paper by Caers, J., Strebelle, S., and Payrazyan, K., Stochastic Integration of Seismic Data and Geologic Scenarios: A West Africa Submarine Channel Saga, The Leading Edge, March 2003, describes how seismically-derived facies probability cubes can be used to further enhance conventional MPS simulation in creating reservoir facies models. A probability cube is created which includes estimates of the probability of the presence of each facies for each cell of the stratigraphic grid. These probabilities, along with information from training images, are then used with a particular MPS algorithm, referred to as SNESIM (Single Normal Equation Simulation), to construct a reservoir facies model.
The aforementioned facies probability cube was created from seismic data using a purely mathematical approach, which is described in greater detail in a paper to Scheevel, J. R., and Payrazyan, K., entitled Principal Component Analysis Applied to 3D Seismic Data for Reservoir Property Estimation, SPE 56734, 1999. Seismic data, in particular seismic amplitudes, are evaluated using Principal Component Analysis (PCA) techniques to produce eigenvectors and eigenvalues. Principal components then are evaluated in an unsupervised cluster analysis. The clusters are correlated with known properties from well data, in particular, interpreted facies, to estimate properties in cells located away from wells. The facies probability cubes are derived from the clusters.
Both variogram-based simulations and the MPS simulation utilizing the seismically-derived facies probability cubes share a common shortcoming. Both simulations methods fail to account for valuable information that can be provided only by geologist/geophysicist's interpretation of the reservoir's geological setting based upon their knowledge of the depositional geology of the region being modeled. This information, in conjunction with core and seismic data, can provide important information on the reservoir architecture and the spatial distribution of facies in a reservoir model.
Probability cubes are also known which, rather than being mathematically derived from seismic data, rely primariliy upon geological interpretation and conceptualization. Examples of commercial facies modeling programs include PETREL®, ROXAR® and HERESIM® programs. The PETREL® program is available from Technoguide AS Corporation of Oslo, Norway. The ROXAR® software is sold by ROXAR ASA Public Limited Company of Stavanger, Norway. The HERESIM® program is available from Institut Francais du Petrole of Cedex, France.
These programs typically combine vertical facies trend information with map or horizontal facies trend informaton to create facies cubes. In some instances, such as with ROXAR®, a modeler inputs equations to describe the probability of finding facies in a vertical section or else in a horizontal or map section or 3D of a model. Alternatively, in other commercial programs such as PETREL®, a modeler may directly digitize a facies probability map wherein the modeler attempts to simultaneously account for the competing presence of all facies in a single map.
Making simultaneous estimates of facies locations and probabilities that are highly dependent upon one, either through digitization or through estimating equations, are complex and challenging. Such methods make it difficult to rapidly create numerous probability cubes based on different geologic interpretations and assumptions of how the facies are distributed in a S-grid. Furthermore, algorithms used to combine vertical and map facies trend information to produce facies probability cubes can produce less than optimal estimates of the probabilities. The present invention addresses these shortcomings in making such facies probability cubes.